Pressing 'Tab' will move certain bones slightly
You have a IK-solver applied on some bones. This constrain does not work in edit mode, so when you go to object/pose mode, constrain starts to affect and moves bones a little. 

Other thing that you show in video - it is bone in the head, it is hidden in edit mode, so you need to press Alt+H to show it.

And by the way, do you know that rigify addon, that you use, has a Rig generator, witch builds all logic for you and you need not to add constraints and additional bones manually?